Question

1/2010x2019-1/2009x2008-1/2008x2007-...-1/3x2-1/2x1 
ae giúp chiều thi r

Answer 1

Ta có : \(\frac{1}{2010.2009}-\frac{1}{2009.2008}-\frac{1}{2008.2007}-.....-\frac{1}{3.2}-\frac{1}{2.1}\)

\(=\frac{1}{2010.2009}-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{2008.2009}\right)\)

\(=\frac{1}{2010.2009}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+......+\frac{1}{2008}-\frac{1}{2009}\right)\)

\(=\frac{1}{2010.2009}-\left(1-\frac{1}{2009}\right)\)

\(=\frac{1}{2010.2009}-1+\frac{1}{2009}=\frac{1}{2010.2009}-\frac{2010.2009}{2010.2009}+\frac{2010}{2010.2009}\)

\(=\frac{1-2010.2009+2010}{2009.2010}=\frac{-4036079}{4038090}\)